Exact top-quark mass dependence in hadronic Higgs production

The impact of the finite top-quark mass on the inclusive Higgs production cross section at higher perturbative orders has been an open question for almost three decades. In this paper, we report on the computation of this effect at NNLO QCD. For the purely gluonic channel, it amounts to $+0.62\mathrm{\%}$ relative to the result obtained in the HEFT approximation. The formally sub-leading partonic channels over-compensate this shift, leading to an overall effect of $-0.32\mathrm{\%}$ at a $pp$ collider energy of $13\mathrm{T}\mathrm{e}\mathrm{V}$, and $-0.16\mathrm{\%}$ at $8\mathrm{T}\mathrm{e}\mathrm{V}$. This result eliminates one of the main theoretical uncertainties to inclusive Higgs production cross section at the LHC.